Gamma-Ray Burst Early Optical Afterglow Modelling

Abstract

We discuss the evolution of a relativistic outflow responsible for producing the emission associated with GRBs. We investigate how afterglows are produced in the inter- action between the outflow and the ambient medium. Understanding the properties of the outflow from afterglow emission can be coupled with information obtained from the prompt component to constrain the magnetisation of the outflow. We analytically and numerically evaluate the relative strength of the reverse shock emission as the out- flow propagates into either a wind or ISM -type environment. We find that previous estimates of magnetisation based on the relative strength of forward and reverse shock emission had been underestimated by up to a factor of 100. We then apply our revised magnetisation estimate to a sample of 10 GRBs and find that 5 of the 10 events can be described by the ISM model. As recent studies have indicated that the fraction of en- ergy stored in the magnetic fields are small, our findings would suggest that the ejecta is driven by thermal pressure. Finally we consider how inhomogeneities present in the outflow can lead to variations in the very early afterglow. Considering small gradi- ent in the ejecta density profile modifies the rising index of the afterglow and can be equivalent to changing the dimensionless parameter ξ by a factor of 2. Uncertainties in determining the width of the ejecta present difficulties in understanding the distribution of GRBs afterglow rising index.